The Urbach tails and optical absorption in layered semiconductor TlGaSe<Subscript>2</Subscript> and TlGaS<Subscript>2</Subscript> single crystals

TlGaSe₂ and TlGaS₂ single crystals were grown by the modified Bridgman-Stockbarger method. We report the result of an experimental study of the optical absorption of TlGaSe₂ and TlGaS₂ crystals. The absorption measurements were performed in steps of 10 K. The direct and indirect band gaps for TlGaSe₂ and TlGaS₂ samples were calculated as a function of temperature. The phonon energies in TlGaSe₂ and TlGaS₂ crystals were calculated as (39±4) and (9±4) meV at 240 K, respectively. At 10 K, direct and indirect band gaps were found as 2.294 and 2.148 eV for TlGaSe₂, 2.547 and 2.521 eV for TlGaS₂ crystals, respectively. The abrupt changes were observed in the direct and indirect band gaps in the some temperature ranges. These changes were interpreted as phase transformation temperatures. The steepness parameters and Urbach energy for TlGaSe₂ and TlGaS₂ samples increased with increasing sample temperature in the range (10–320) K.     

Structural phase transitions in Fe3+ -doped ferroelectric TlGaSe2 crystal

This paper presents the results of dielectric constant and Electron Paramagnetic Resonance (EPR) investigations of Fe³⁺-doped TlGaSe₂ single crystals in the temperature range of 15–300 K. The influence of Fe impurities on dielectric properties and phase transitions of TlGaSe₂ crystal has been studied. The results were considered in comparison with earlier observed results from pure TlGaSe₂ compounds. We observed the considerable decrease of the dielectric constant as well as the change of the shape of the temperature dependence of the dielectric constant in doped crystals. Some certain significant changes of EPR spectra, which are associated with a strong splitting and appearance of additional resonance lines, were observed at the temperatures below 110 K. Such transformations are considered as the result of non-equivalent displacements of different groups of Tl atoms during the structural phase transitions.     

Specific features of the formation of the ferroelectric phase in polytypes of TlGaSe2 crystals

The polytypism of layered crystals of thallium gallium diselenide TlGaSe₂ has been found to substantially affect the temperature of phase transformations and the mechanism of formation of the polar state in these ferroelectrics. In particular, it is shown that the phase transition observed in the C-TlGaSe₂ polytype is an improper ferroelectric phase transition occurring at a temperature T _c ≈ 108 K, whereas the phase transition observed in the 2C-TlGaSe₂ polytype is a proper ferroelectric phase transition occurring at a higher temperature T _c ≈ 111 K. It is concluded that the elucidation of the polytype of a particular sample is a necessary stage of investigation of the TlGaSe₂ crystals.     

Anisotropy of the hopping conductivity in TlGaSe2 single crystals

The temperature dependences of the conductivities parallel and perpendicular to the layers in layered TlGaSe₂ single crystals are investigated in the temperature range from 10 K to 293 K. It is shown that hopping conduction with a variable hopping length among localized states near the Fermi level takes place in TlGaSe₂ single crystals in the low-temperature range, both along and across the layers. Hopping conduction along the layers begins to prevail over conduction in an allowed band only at very low temperatures (10–30 K), whereas hopping conduction across the layers is observed at fairly high temperatures (T?210 K) and spans a broader temperature range. The density of states near the Fermi level is determined, N _F=1.3×10¹⁹eV·cm³)^?1, along with the energy scatter of these states J=0.011 eV and the hopping lengths at various temperatures. The hopping length R along the layers of TlGaSe₂ single crystals increases from 130 Å to 170 Å as the temperature is lowered from 30 K to 10 K. The temperature dependence of the degree of anisotropy of the conductivity of TlGaSe₂ single crystals is investigated.     

Phase-matched second-harmonic generation due to thermal expansion of TlGaSe2 layered crystal

Second-harmonic generation effects have been investigated in TlGaSe₂ layered crystal over a temperature range where ferroelectric phase exists. Pronounced periodical changes of the second-harmonic signal with temperature have been discovered. The observed effect is explained within the phase synchronism condition which changes with the temperature. The main mechanism of the thermal expansion of the sample in the observed phenomenon is explained.     

Phase transitions and metastable states in TlGaSe2

The results of measurements of the dielectric constant of TlGaSe₂ in temperature range of successive phase transitions are presented. An anomaly in the temperature dependence of the real part of dielectric constant in TlGaSe₂ has been observed at about 242?K in addition to anomalies at 115, 108, and also near 65?K as reported in previous publications. The presence of temperature hysteresis effects in temperature interval between 115 and 242?K allowed making a conclusion about possible existence of an incommensurate phase in the mentioned temperature range. A model of succession of the structural phase transitions in TlGaSe₂ has been suggested.     

Effect of lattice deformation and phase transitions on the electronic spectra of TlGaS<Subscript>2</Subscript>, TlGaSe<Subscript>2</Subscript>, and TlInS<Subscript>2</Subscript> layered semiconductors

The effect of the lattice deformation on the electronic spectra of TlGaS₂, TlGaSe₂, and TlInS₂ layered semiconductor crystals is analyzed. It is shown that changes in the band gap of these semiconductors due to thermal expansion and a change in the composition under hydrostatic or uniaxial pressure can be described within a unified model of the deformation potential. The main feature of this model is the inclusion of deformation potentials with different signs, which is characteristic of other semiconductors with a layered structure. An analysis of the lattice deformation of the studied semiconductors in terms of the proposed model of the deformation potential has revealed that, in the immediate vicinity of the phase transitions, the crystal lattice under pressure undergo an unusual deformation.     

The Growth of P-type TlGaSe2(1−x) S2x Single Crystals

TlGaSe_2(1–x) S_2x single crystals were grown by the modified Bridgman-Stockbarger method in our crystal growth laboratory. A^IIIB^III C₂ ^VI compounds are formed of elements from vertical groups of the periodic table (group III: Tl, Ga, In; group VI: Se, S, Te) and are classified into two types. The first type has a layer structure: TlGaSe₂, TlGaS₂ and TlInS₂. The second type has a chained structure: TlInSe₂, TlInTe₂ and TlGaTe₂. None of the grown crystals had cracks and voids on the surface. The freshly cleaved crystals had a mirror-like surface and there was no need for mechanical or chemical polishing treatments. By the hot probe technique, we have found that the crystals were of p-type. The ingots produced were single crystalline and the useful region of single crystal was 90% with steps of 10 K if changes were small, and with steps of 3 and 5 K if changes were large in the direct and indirect band gaps energies. The direct and indirect band gaps for TlGaSe_2(1–x)S_2x samples were calculated as a function of temperature.     

Low-temperature anomalies in thermal expansion of HTSCs: System Bi2Sr2−x LaxCuO6

The data on thermal expansion at low temperatures have been obtained for HTSC single crystals of the system Bi₂Sr_2?x La_xCuO₆ with different doping levels. Anomalous (negative) thermal expansion is observed in the temperature range from 5 to 20 K. It is shown that the anomaly vanishes in an overdoped sample. An anomalously strong effect of magnetic fields of 2–4 T on the negative thermal expansion domain is observed. The effect of field screening, frozen field, doping level, defects and oxygen vacancies on the region of thermal expansion anomalies is investigated. The origin of the observed anomalies in the properties of the system Bi₂Sr_2?x La_xCuO₆, as well as other HTSC systems in which similar anomalies have been observed, is discussed.     

Electret states and the phase transition in a surface layer of the TlGaSe2 ferroelectric semiconductor

The electret polarization is investigated in the TlGaSe₂ ferroelectric semiconductor. It is proved for the first time that stable internal electric fields associated with residual electret polarization are induced in crystals of the TlGaSe₂ ferroelectric semiconductor at temperatures T < 200 K. It is experimentally established that the peak of the pyroelectric current measured in the vicinity of the phase transition to the ferroelectric polar phase depends substantially on the temperature at which the external electric field is switched off when the TlGaSe₂ ferroelectric crystal under investigation is preliminarily cooled from room temperature. The results obtained are discussed in the framework of a model according to which internal electret fields are induced by charges localized at different levels in the bulk and on the surface of the TlGaSe₂ ferroelectric crystal. These fields drastically change at temperatures in a narrow range near 135 K. The inference is made that a phase transition occurs in the surface layer of the TlGaSe₂ crystal at a temperature close to ～135 K.     

Spectroscopic ellipsometry study of above-band gap optical constants of layered structured TlGaSe2, TlGaS2 and TlInS2 single crystals

Spectroscopic ellipsometry measurements on TlGaSe₂, TlGaS₂ and TlInS₂ layered crystals were carried out on the layer-plane (0 0 1) surfaces, which are perpendicular to the optic axis c^?, in the 1.2–6.2 eV spectral range at room temperature. The real and imaginary parts of the pseudodielectric function as well as pseudorefractive index and pseudoextinction coefficient were found as a result of analysis of ellipsometric data. The structures of critical points in the above-band gap energy range have been characterized from the second derivative spectra of the pseudodielectric function. The analysis revealed four, five and three interband transition structures with critical point energies 2.75, 3.13, 3.72 and 4.45 eV (TlGaSe₂), 3.03, 3.24, 3.53, 4.20 and 4.83 eV (TlGaS₂), and 3.50, 3.85 and 4.50 eV (TlInS₂). For TlGaSe₂ crystals, the determined critical point energies were assigned tentatively to interband transitions using the available electronic energy band structure.     

Wärmeausdehnung von H2O- und D2O-Einkristallen

The linear thermal expansion coefficients of ice and heavy ice single crystals have been measured in both hexagonal crystallographic axes between the melting point and 18° K. The expansion coefficients of H₂O and D₂O become negative below 63° K.     

Time relaxation of dielectric constant in the commensurate phase of TlGaSe2

The results of measurements of the time dependences of the dielectric constant of TlGaSe₂ in the commensurate ferroelectric phase are presented. From the result of the observation of the decay of ε at different stabilized temperatures below the commensurate phase transition temperature after cooling from the incommensurate phase, the presence of two different characteristic relaxation time constants with the same temperature behaviour has been revealed. This peculiarity is considered as a result of a coexistence of two polar sublattices in the temperature range below 110 K. According to these results, the previously reported dielectric anomaly at about 103 K is considered as a final lock-in phase transition accompanied by the forming of the antiferroelectric state in TlGaSe₂.     

Anomalous behaviour of the Urbach edge and phase transitions in TlGaSe2

The long-wavelength tail of the optical absorption in TlGaSe₂, crystals at α=30−150cm^-1 is shown to obey Urbach's rule in the temperature range 4.2–294°K. The anomalous behaviour of the parameters of this rule suggests the presence of two phase transitions in TlGaSe₂ at 246°K and 101°K beside the known phase transitions at 120°K and 107°K. The presence of phase transitions in TlGaSe₂ at 246°K and 101°K is also confirmed by means of the heat capacity measurement.     

Raman spectra of TlGaSe<Subscript>2</Subscript> single crystals

The results of the study of the Raman spectrum of TlGaSe₂ single crystals are presented. The ability of these layered crystals to cleave into plates with mirror faces, being a consequence of significant asymmetry of the chemical bond, makes them promising materials for photoelectric converters.     

Thermal hysteresis and memory effects in TlGaSe2 crystal with incommensurate phase

Temperature dependencies of dielectric permittivity of TlGaSe₂ have been measured under various thermal cycles. Peculiarities of anomalies in temperature dependencies of dielectric permittivity corresponding to structural phase transitions at 108 and 115?K are discussed. The coexistence of two different incommensurate structures in TlGaSe₂ was proposed. The phase transitions at 108 and 115?K are considered as commensurate lock-in transitions. As a result a new model of the structural phase transitions in TlGaSe₂ has been suggested.     

Photoluminescence spectra of TlGaSe<Subscript>2</Subscript> semiconductor structures

The results of the study of photoluminescence and its excitation spectra in TlGaSe₂ single crystals are presented. The ability of these layered crystals to be cleaved by plates with mirror faces, being a consequence of sharp asymmetry of the chemical bond, makes them promising materials for photoelectric converters.     

Heat capacity and thermal expansion of CdCr2Se4 and CdCr2S4

The thermodynamic properties of the spinel ferromagnetic compounds CdCr₂Se₄ and CdCr₂S₄ have been investigated by making heat capacity and thermal expansion measurements on single crystals. For both compounds, the ferromagnetic transition is marked by λ-type thermal anomalies, and the results provide a pressure dependence of the transition temperatures that is in agreement with direct measurements. Below the transition, CdCr₂S₄ shows an anomalous heat-capacity contribution and negative thermal expansion, which are in contrast to the conventional behavior found in CdCr₂Se₄.     

Defects forming the optical absorption edge in TlGaSe2 layered crystal

In this work, we present the results of optical experiments designed to investigate the changes in optical absorption spectra of TlGaSe₂ ferroelectric-semiconductor with incommensurate (INC) phase in experimental conditions where crystal is kept several hours within the INC-phase (the regime of so called “memory” effect). The fundamental absorption of TlGaSe₂, experimentally investigated by optical transmission measurements performed in the temperature range 15–300 K. An extraordinary modification of the optical absorption edge in the range of Urbach's tail is discovered as a result of the annealing within the INC-phase. The role of native defects forming the band edge in the observed phenomena in TlGaSe₂ is discussed.     

EPR spectra of Fe centers in layered TlGaSe2 single crystal

A single-crystal TlGaSe₂ doped by paramagnetic Fe ions has been studied at room temperature by electron paramagnetic resonance (EPR) technique. The fine structure of EPR spectra of paramagnetic Fe³⁺ ions was observed. The spectra were interpreted to correspond to the transitions among spin multiplet (S=5/2, L=0) of Fe³⁺ ion, which are splitted by the local ligand crystal field (CF) of orthorhombic symmetry. Four equivalent Fe³⁺ centers have been observed in the EPR spectra and the local symmetry of crystal field at the Fe³⁺ site and CF parameters were determined. Experimental results indicate that the Fe ions substitute Ga at the center of GaSe₄ tetrahedrons, and the rhombic distortion of the CF is caused by the Tl ions located in the trigonal cavities between the tetrahedral complexes.